Colloqial idiomatic metaphor for incomplete logic?

Question

Seems like[1] I vaguely recall some colorful expression for conveying a rhetorical failure to complete a logical argument. Something along the lines of “failing to tie the knot” or “complete the circle,” although those possess other established definitions. Am I hallucinating or did someone perhaps misapply those expressions? Or is there a more apropos idiom?

EDIT: I’ve been asked to edit my question if I wish to clarify any distinction w.r.t. an extant question which seeks terms that apply to leaps in logic that form an identifiable logical fallacy such as a meretricious, eristic, specious, sophistic argument could be a form of cherry picked syllogistic fallacy, tautology or perhaps even strawmanning. Whereas, my question seeks a term that applies to a failure to even complete and put forth a fully formed logical argument aka contingency, which could then be judged to be a fallacy or not. Without a clearly articulated logical proposition, one is adrift trying to figure out what the attempted logical assertion might actually be. The leap in my case being not a specifically identified fallacy of logic, but for example a possibly serpentine, desultory, circumlocutory narrative that may lull the naive into thinking some enumerated, identifiable (aka cogent) argument was presented when it wasn’t.

The motivating case for my question was a comment I wrote about a recent CNBC video The Recession Has Finally Begun, But Only For America's Rich | CNBC:

Where is the aggregate, hard data demonstrating the spending (and investment activities?) of high net worth individuals predominately drive the GDP? You do state the power-law distribution driven Pareto effect at 6 minutes that the top 20% BY INCOME drive half the consumer spending, but your analysis is too crude. What if the lower 80% are increasing their spending due to government handouts and increases in the minimum wage? Or maybe the high income earners’ spending affects some sectors of disproportionately (e.g. discretionary, luxury goods and financed investment assets including venture capital startups) compared to the sectors that the lower 80% prop up (e.g. staples such as food). If the government is borrowing and spending like no tomorrow, maybe the flood of money into spending may just continue defying conventional (incomplete logic) expectations. Or at least you should nuance the argument more as to how we may end up in stagflation with the inflation in non-discretionary and stagnation in discretionary or speculative assets at least until the Fed is forced to turn on the cheap money spigot again but they will only do so when the money printing can be sanitized by trapping all speculation inside of “not your keys, not your tangible, not your assets” capital controls aka central bank digital currencies and the end of cash (except for the USD because that would end it as the reserve currency if they can cancel tangible dollars). Another factor is you cite high income but that is the upper middle class, not the uber high net worth. High net worth individuals spend a very small percentage of their net worth on consumption (other than maybe big ticket maintenance such as their villas, yachts and private planes). Your ostensibly ignoratio elenchi, thought-terminating cliché, meretricious, rhetorical narrative fails to articulate a coherent and complete thesis that can be coherently applied to predicting our future. You fail to logically tie the knot or complete the circle. Your possibly eristic, specious, sophistic argument could be a form of cherry picked syllogistic fallacy. You fail to articulate a replete, coherent logical contingency thus your statements could be a tautology. I think you (CNBC) need to undertake some philosophy courses in logic.

---

[1] My potentially congenital jaundice liver, adult NAFLD, Tuberculosis, endocrine dysfunction driven brain-fog apophenia kicking in again perhaps.

Answer 1

Tinfoil Hat's suggestion seems the most fitting answer; I'm not sure why it's not given as one.

Drawing the wrong conclusion (itself a fixed phrase, though hardly a colloquialism) when applying deductive reasoning is often denounced as

• putting two and two together and getting five

and correspondingly failing to draw a fairly obvious conclusion is

• not putting two and two together.

put two and two together [idiom]

... to figure something out

[Merriam-Webster]

The phrase to put two and two together means:

to draw an inference (especially an obvious inference) from available evidence....

I found my first grey hairs in my late 20s and by the time I reached 40 I was colouring it every third week. My face started swelling up every three weeks, and I didn’t put two and two together until a mum at school told me it was the hair dye. [ Sophie de Rosée, Daily Telegraph, Nov 2013]

[WordHistories]

Answer 2

... my question seeks a term that applies to a failure to even complete and put forth a fully formed logical argument aka contingency, which could then be judged to be a fallacy or not.

---

I suggest the idiomatic phrase jump to conclusions / jump to a conclusion, more formally known as the fallacy of faulty generalization.

jump to a conclusion (phrase)

If you say that someone jumps to a conclusion, you are critical of them because they decide too quickly that something is true, when they do not know all the facts.
Collins

jump to conclusions (idiom)

To guess the facts about a situation without having enough information.
Cambridge

jump to a conclusion

Form an opinion or judgment hastily, as in Wait till you have the facts; don't jump to a conclusion. [c. 1700]
dictionary.com

---

Fallacy of hasty generalization. We "jump to a conclusion" on the basis of a single or only a few instances. For example: Physicians make judgments on the basis of only a few characteristics.
Barbara Maier and Warren Shibles; The Philosophy and Practice of Medicine and Bioethics (2010)

Readers are inclined to the fallacy of faulty generalization when they jump to a conclusion without enough evidence to support it.
James Thomas; Script Analysis for Actors, Directions, and Designers (2023)

Logicians, those who study the principles of correct reasoning, have a term for the kind of bad reasoning involved in our examples of typecasting and stereotyping from Lynch's work. They call it a fallacy, and the thinking involved, fallacious reasoning. Fallacies occur whenever we jump to a conclusion, namely, when we incorrectly, illegitimately, or inappropriately draw a conclusion from reasons that don't support conclusion.
William Devlin and Shai Biderman; The Philosphy of David Lynch (2011)

Generalization, we know, is a credible inductive procedure when properly done. We use it all the time in ordinary life as well as in sciences. However, sometimes people generalize too hastily from a few instances of simply from one instance to the whole class. The sample is not representative enough. This makes the grounds of the conclusion too narrow and flimsy. As a result the conclusion does not really follow from the narrow data. Engaging in this type of reasoning commits the fallacy of hasty generalization.
M. Ashraf Adeel; Fallacies in Reasoning (2021)